On Universal Cycles of Labeled Graphs

Greg Brockman, Bill Kay, Emma E. Snively

Abstract

A universal cycle is a compact listing of a class of combinatorial objects. In this paper, we prove the existence of universal cycles of classes of labeled graphs, including simple graphs, trees, graphs with $m$ edges, graphs with loops, graphs with multiple edges (with up to $m$ duplications of each edge), directed graphs, hypergraphs, and $k$-uniform hypergraphs.